You're correct -- many of the Iranian marchers in Westwood, CA, ARE Jewish. On the other hand, some are just very moderate Muslims, like my former neighbor, a lovely young woman who was educated in the U.S. along with her brother while their parents stayed in Iran and have suffered greatly at the hands of the fanatics there. She had the most horrifying stories of her return visits to Iran in recent years...
From what I understand, the Shah was trying to do for Iran what Ataturk did for Turkey-- give the country freedom of religion and remove the Islamist stranglehold on the government.
Someday, Iran may well rename themselves Persia and many will return to the logical religion of that great Empire before Islam was imposed by the sword. Aren't the Baha's an attempt to harmonize Zorastism (which was also the religion of the three kings who visited the Christ child), Islam, Christianity and Judaism?
I also heard the name Persia was changed to Iran during World War II to placate Hitler as it meant the land of the Aryans. True or urban legand?